Shortest Path Problems on a Polyhedral Surface

Abstract

We develop algorithms to compute edge sequences, Voronoi diagrams, shortest
path maps, the Fréchet distance, and the diameter for a polyhedral surface. Distances on the surface are measured either by the length of a Euclidean shortest path or by link distance. Our main result is a linear-factor speedup for computing all shortest path edge sequences on a convex polyhedral surface.